Mathematical Sciences: Foundations and Applications of Bayesian Inference and Decision Theory

数学科学：贝叶斯推理和决策理论的基础和应用

• 批准号: 9201056
• 负责人: Bruce Hill
• 金额: $ 6万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1995-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201056&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Foundations; Applications; Bayesian

This project addresses Bayesian nonparametric procedures which incorporate information about the mean and about the tail behavior of the sampling distribution. Extensions to non-random samples from finite populations may be developed, drawing on a Bayesian theory of randomization. Extensions for censored data in the presence of covariates should also follow. Foundational issues for Bayesian theory of statistical inference revolve around assembling past information or prior opinion with new information or data and then presenting the amalgamated view. The inclusion of subjective views with information from observations has important implications for the applications of Bayesian inference and for effective statistically-based prediction and decisions. This research examines both fundamental mathematical issues and their applications to specific scientific questions.

本专题讨论贝叶斯非参数程序 它包含了关于均值和尾部的信息 抽样分布的行为。 非随机扩展 从有限的人口样本可以开发，借鉴一个 贝叶斯随机化理论。 删失数据的扩展 在存在协变量的情况下，也应该遵循。 贝叶斯统计理论的基础问题 推理围绕着过去信息或先验知识的组合 新的信息或数据，然后提出意见， 混合视图。 纳入主观观点， 从观测中获得的信息对以下方面具有重要意义： 贝叶斯推理的应用和有效的 基于知识的预测和决策。 本研究 研究了基本的数学问题及其 应用于具体的科学问题。